Probabilistic memory-one strategies to dominate the iterated prisoner’s dilemma over networks

Abstract

The Iterated Prisoner’s Dilemma (IPD) has been a classical game theoretical scenario used to model behaviour interactions among agents. From the famous Axelrod’s tournament, and the successful results obtained by the Tit for Tat strategy, to the introduction of the zero-determinant strategies in the last decade, the game theory community has been exploring the performance of multiple strategies for years. This article grounds on such previous work, studying probabilistic memory-one strategies (PMO) and using evolutionary game theory, to analyse the criteria to find the most successful set of strategies in networked topologies. The results are nearly deterministic in discrete PMO scenarios. However, results become much more complex when moving to continuous ones, and there is no optimal strategy for a given scenario. Finally, this article describes how, using machine learning and evolutionary techniques; a cluster of agents, playing synchronously and adaptively, is able to dominate the rest of the population.